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arXiv:2407.20984 · Physical Review A

Engineering photonic band gaps with a waveguide-QED structure containing an atom-polymer array

M. S. Wang, W. Z. Jia

Published Nov 26, 2024• 6 citations
arXivHTMLPDF

Abstract

We investigate the generation and engineering of photonic band gaps in waveguide quantum electrodynamics systems containing periodically arranged atom polymers. We first consider the configuration of a dimer array coupled to a waveguide. The results show that if the intra- and intercell phase delays are properly designed, the center and the width of the band gaps, as well as the dispersion relation of the passbands, can be modified by adjusting the intracell coupling strength. These manipulations provide ways to control the propagating modes in the waveguide, leading to some interesting effects such as slowing or even stopping a single-photon pulse. Finally, we take the case of the tetramer chain as an example to show that, in the case of a larger number of atoms in each unit cell, tunable multigap structures and more sophisticated band-gap engineering can be realized. Our proposal provides efficient ways for photonic band-gap engineering in micro- and nanoquantum systems, which may facilitate the manipulation of photon transport in future quantum networks.

DOI
10.1103/physreva.110.053716

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We investigate the generation and engineering of photonic band gaps in waveguide quantum electrodynamics systems containing periodically arranged atom polymers. We first consider the configuration of a dimer array coupled to a waveguide. The results show that if the intra- and intercell phase delays are properly designed, the center and the width of the band gaps, as well as the dispersion relation of the passbands, can be modified by adjusting the intracell coupling strength. These manipulations provide ways to control the propagating modes in the waveguide, leading to some interesting effects such as slowing or even stopping a single-photon pulse. Finally, we take the case of the tetramer chain as an example to show that, in the case of a larger number of atoms in each unit cell, tunable multigap structures and more sophisticated band-gap engineering can be realized. Our proposal provides efficient ways for photonic band-gap engineering in micro- and nanoquantum systems, which may facilitate the manipulation of photon transport in future quantum networks.
If the electromagnetic waves are scattered by the periodic structure of media with different refractive indexes, a band gap in the transmitted spectrum can be generated. This is the photonic crystal whose band gap is usually uncontrollable as its structure parameters are fixed after the fabrication. Alternatively, based on the quantum theory in real space for single photons transporting along a one-dimensional waveguide embed by a series of two-level atoms, we propose here a quantum mechanical configuration to implement the photonic crystal with adjustable band gap. It is shown that if the scattering two-level atoms are arranged as a periodic array, the desirable band gap in the photonic transmission spectrum can be formed. This is the atomic-type photonic crystal, in which the center frequency of the gap can be controlled by adjusting the eigenfrequencies of the atoms. The possible physical implementations of our proposal with the voltage-biased superconducting qubits for the centimeter waves and the voltage-biased electrons on liquid helium for the millimeter waves are also discussed.
We theoretically study the single-photon transport properties in periodic and position-disordered Jaynes–Cummings (or JC) arrays of waveguide-coupled microtoroidal ring resonators, each interacting with a single two-level quantum emitter. Employing the real-space formalism of quantum optics, we focus on various parameter regimes of cavity quantum electrodynamics (cQED) to gain better control of single-photon propagation in such a many-body quantum optical setting. As for some of the key findings, we observe that the periodic setting leads to the formation of the band structure in the photon transmission spectra, which is most evident in the strong coupling regime of cQED. However, under resonant conditions with no losses, the application of Bloch’s theorem indicates that the width of forbidden gaps can be altered by tuning the emitter-cavity coupling to small values. Moreover, in the disordered case, we find that the single-photon transmission curves show the disappearance of band formation. However, spectral features originating from cQED interactions observed for the single atom-cavity problem remain robust against weak-disordered conditions. The results of this work may find application in the study of quantum many-body effects in the optical domain as well as in different areas of quantum computation and quantum networking.
We present a scheme for achieving broadband complete reflection by constructing photonic band gap via collective atom-atom interaction in a one-dimensional (1D) waveguide quantum electrodynamics (QED) system. Moreover, we propose several strategies to further expand the ultrahigh-reflection windows, including increasing the number of atoms with separations near the Bragg distance and inducing gradient frequency modulation among the atoms. The center frequency and bandwidth of the ultrahigh-reflection window are dynamically adjustable by applying external electromagnetic field. The results here can enrich the many-body physics of the waveguide-QED system and offer a pathway for achieving broadened ultrahigh reflection in a controllable way, which can find important applications in the realms of chip-integrated band filter, quantum storage, optical switching, and wavelength-selective devices.
Waveguide quantum electrodynamics (QED) provides a powerful framework for engineering quantum interactions, traditionally relying on periodic photonic arrays with continuous energy bands. Here, we investigate waveguide QED in a fundamentally different environment: A one-dimensional photonic array whose hopping strengths are structured aperiodically according to the deterministic Fibonacci-Lucas substitution rule. These "Fibonacci waveguides" lack translational invariance and are characterized by a singular continuous energy spectrum and critical eigenstates, representing a deterministic intermediate between ordered and disordered systems. We demonstrate how to achieve decoherence-free, coherent interactions in this unique setting. We analyze two paradigmatic cases: (i) Giant emitters resonantly coupled to the simplest aperiodic version of a standard waveguide. For these, we show that atom photon bound states form only for specific coupling configurations dictated by the aperiodic sequence, leading to an effective atomic Hamiltonian, which itself inherits the Fibonacci structure; and (ii) emitters locally and off-resonantly coupled to the aperiodic version of the Su-Schrieffer-Heeger waveguide. In this case the mediating bound states feature aperiodically modulated profiles, resulting in an effective Hamiltonian with multifractal properties. Our work establishes Fibonacci waveguides as a versatile platform, which is experimentally feasible, demonstrating that the deterministic complexity of aperiodic structures can be directly engineered into the interactions between quantum emitters.
Spatial gaps correspond to the projection in position space of the gaps of a periodic structure whose envelope varies spatially. They can be easily generated in cold atomic physics using finite-size optical lattice, and provide a new kind of tunnel barrier which can be used as a versatile tool for quantum devices. We present in detail different theoretical methods to quantitatively describe these systems, and show how they can be used in one dimension to realize matter wave Fabry-Perot cavities. We also provide experimental and numerical results that demonstrate the interest of spatial gap structures for phase space engineering. We then generalize the concept of spatial gaps in two dimensions and show that this enables one to design multiply connected cavities which generate a quantum dot structure for atoms or allow one to construct curved wave guides for matter waves. At last, we demonstrate that modulating in time the amplitude of the periodic structure offers a wide variety of possible atom manipulations including the control of the scattering of an incoming wave packet, the loading of cavities delimited by spatial gaps, their coupling by multiphonon processes or the realization of a tunable source of atoms. This large range of possibilities offered by space and time engineering of optical lattices demonstrates the flexibility of such band-gap structures for matter wave control, quantum simulators, and atomtronics.
Photonic state engineering in waveguide QED is typically based on local light-matter interactions. This limits its control over the spatial structure of bound photonic states. Here, we demonstrate a distinct mechanism arising from the interplay between nonlocal giant-atom coupling and topological band structure. Specifically, we consider giant atoms coupled to a Su-Schrieffer-Heeger waveguide and show that this configuration enables a controllable energy-level crossing protected by the topological gap. Adiabatically sweeping the atomic detuning across the crossing leads to a controlled exchange between distinct photonic bound states. In a two-giant-atom configuration, this mechanism achieves high-fidelity conversion of a spatially splitting state into a combining state. Extending this scheme to three-giant atoms, we further realize robust, shape-preserving photon transfer mediated by sequential in-gap crossings. Our results demonstrate how topology and nonlocal light-matter coupling can be combined to achieve programmable control of bound photonic states in waveguide QED platforms.